Questions (pt 1)

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Big Idea

The difficulty (and importance) of enacting cognitively challenging (or high-level) tasks. Also, if the curriculum doesn't provide them, the challenge of transforming tasks so that they are cognitively challenging.

Prospective Teachers

  • What is (or should be) the role of curriculum materials (K-12) in teacher preparation? How are they being used in courses for teacher prep? What do preservice teachers learn about the use of curriculum materials in courses that use materials in various ways?
  • How do preservice teachers' ideas about curriculum change over time?
  • How do field experiences impact preservice teachers' understanding and use of curriculum materials?
  • How does the learning of a single curriculum compare to learning multiple curriculum? Is there value to seeing a single curriculum in depth even if it's not going to be used?
  • What is taught in required math courses for prospective elementary teachers? What is taught in the math methods courses? What is the overlap? Where are the gaps?
  • What do prospective teachers learn about knowledge for teaching (math content, lesson planning, flexibility) from various "treatments/instantiations" of content courses and methods courses?
    • Which treatments seem most effective?
    • What are typical learning trajectories?

Practicing Teachers

  • What is the minimum number of classroom observations needed to provide a reliable profile of whatever aspects of curriculum is being measured?
  • How are teachers' conceptions of the mathematical storyline of a lesson/unit/text related to the enacted curriculum? How does the enacted curriculum influence the conceptions?
  • What role do curriculum materials play in teacher learning of content?

Mathematical Knowledge for Teaching

  • Under the assumption that math content matters, what and how much math do prospective teachers need? What is the evidence that this knowledge effects their ability to implement curricula effectively?
  • What is the nature of the support information provided in the curriculum materials with respect to MKT? (E.g., do they explicitly state the mathematical goals of the lesson? Do they provide info about common student misconceptions or how to address them?) In what ways can that kind of info help teachers develop well-connected MKT? In what ways can that kind of info impact curriculum implementation and student learning?

Pedagogical Knowledge and Practices


Context and Resources

  • What context provides the best opportunity for learning -- 2 x 2 teacher beliefs (trad. vs. ref.) and curriculum orientation (trad. vs. ref.)? How do you study this alignment?
  • What factors influence materials adoption at the high school level? What are results? What P.D.? Fallout?
  • How do we characterize curricula to determine the extent to which they afford activities related to learning for understanding (e.g., connections, learning trajectories, sense making)?
  • What factors influenced high schools that reorganized their math sequence and adopted integrated curriculum? (Document their experience - tensions, obstacles, strategies, successes, etc.)
  • How do changes in state mandates (or conflicts b/w different levels of mandates) relate to teachers' decisions about how to use curriculum materials? (i.e., different inputs to what is ultimately the enacted curriculum)
  • Could we develop a contingency table for school districts, based on research (existing or growing out of this project), that takes as input particular features of the district and their desired outcomes and gives as output recommendations of curriculum materials?

Vertical Slices

  • How do practicing teachers' beliefs about and uses of curricula influence pre-service teachers' emerging beliefs about and uses of curricula?
  • How do we prepare preservice and inservice teachers mathematically to cope with all of the variability in curricula they are bound to face in their professional lives?